The determination of the time delay between two signals, one reference and one shifted is performed in many fields of practice including, but not limited to: medical imaging, RADAR, SONAR and speech processing. Such determinations are referred to as time delay estimation (TDE), and, among medical imaging fields includes use in many medical ultrasound modalities, including, but not limited to: blood flow estimation, phase aberration correction, elastography, tissue elasticity estimation, and acoustic radiation force imaging.
Because of its broad application, many algorithms for TDE have been devised. These methods aim to optimize accuracy, precision, computational efficiency, delay range, and noise performance, among other criteria.
In general, TDE algorithms employ pattern-matching functions to estimate the optimal delay between two or more discretely sampled signals, e.g., see Giunta G., “Fine estimators of two-dimensional parameters and application to spatial shift estimation”, IEEE Trans Signal Processing 1999; 47(12):3201-3207; and Jacovitti et al., “Discrete time techniques for time delay estimation”, IEEE Trans Signal Processing 1993; 41(2):525-533, both of which are hereby incorporated herein, in their entireties, by reference thereto. Regardless of the particular pattern-matching function used, all TDE algorithms exhibit an intrinsic bias and variance.
The bias of an estimator is defined as the difference between the expected value of that estimator and the tale value of the variable that is being estimated.
The estimator variance is a function of two types of errors—false peak errors and jitter errors. False peak errors occur at integer multiples of the signal period and generally occur with low probability under reasonable imaging parameters and conditions. Because they occur with low probability and are easily distinguishable, these errors may be readily identified and removed. In contrast, jitter errors are generally small in magnitude and represent a fundamental limit on performance for a given set of imaging parameters, signal-to-noise ratio (SNR), and signal correlation.
While both electronic noise and signal decorrelation degrade TDE performance, they result from different physical phenomenon and generally possess different frequency spectra. Electronic noise, which is generally considered to be a random process, originates from thermal noise in resistors, quantization noise in A/D converters, and intrinsic amplifier noise. Because electronic noise is considered to be random, it is typically modeled as additive noise with a uniform power spectrum. In contrast, echo decorrelation results from the varying echo contributions from different scatterers between different signal acquisitions. In radiation force imaging for example, a gradient of deformations across the point spread function (PSF) causes signal decorrelation, which in turn leads to corruption of TDE estimates and an underestimation of peak displacement, e.g., see McAleavey et al., “Estimates of echo correlation and measurement bias in acoustic radiation force impulse imaging”, IEEE Trans Ultrason Ferroelect Freq Contr 2003; 50(6):631-641; Palmeri et al., “Ultrasonic tracking of acoustic radiation force-induced displacements in homogeneous media”, IEEE Trans Ultrason Ferroelect Freq Contr 2006; 53(7): 1300-1313; and Viola et al., “Ultrasound echo decorrelation due to acoustic radiation force”, IEEE Ultrason Symp 2002; 2:1903-1906, each of which is incorporated herein, in its entirety, by reference thereto, respectively.
Along with fixed imaging parameters such as the center frequency and bandwidth of signals that are transmitted to an object to be measured as to motion, and signals (echo signals) that are received as reflected from the object, the performance of motion estimation is reliant upon its imaging environment. In particular, the correlation of the translated echo signals and the signal-to-noise ratio (SNR) are especially important factors.
To reduce the effects of noise and decorrelation, and therefore improve TDE performance, signal separation techniques may be employed prior to TDE. Finite impulse response (FIR) and infinite impulse response (IIR) filters have been used to improve SNR. However, these frequency domain-based techniques are unable to separate signals with overlapping spectra, and therefore, are generally ineffective in reducing signal decorrelation.
In contrast, regression filters offer an alternative approach that assumes that signals are the summation of polynomials in the time domain, e.g., see Kadi et al., “On the performance of regression and step-initialized iir clutter filters for color Doppler systems in diagnostic medical ultrasound”, IEEE Trans Ultrason Ferroelec Freq Control 1995; 45(3):837-851, which is hereby incorporated herein, in its entirety, by reference thereto. The utility of regression depends heavily upon the selection of the polynomial constituents forming the signal basis. While the polynomial basis for regression filtering can be formed from an a priori model of previous data examples, this strategy is typically not feasible in medical ultrasound where different tissue structures and imaging parameters dramatically change the statistical structure of received data. Instead, adaptively forming the polynomial signal basis is a more appropriate approach.
In the field of medical ultrasound, adaptive regression filtering has been demonstrated via blind source separation (BSS) techniques applied to clutter rejection, e.g., see Gallippi et al., “Complex blind source separation for acoustic radiation force impulse imaging in the peripheral vasculature, in vivo”, IEEE Ultrasonics Symposium 2004; 1:596-601, which is incorporated herein, in its entirety, by reference thereto. However, the method of Gallippi et. al. addresses motion-independent clutter (i.e., clutter/noise that is not generated by the act of motion itself). Further, the method of Gallippi et al. requires comparison of signal components to identify spatial variations that correspond to relative spatial locations of the different types of target being monitored (e.g., vessel walls vs. blood) and therefore requires user input and is not an automatic process. Further BSS techniques are described in Gallippi et al., “Adaptive clutter filtering via blind source separation for two-dimensional ultrasonic blood velocity measurement”, Ultrason Imag 2002; 24(4):193-214; and in; Gallippi et al., “BSS-based filtering of physiological and ARFI-induced tissue and blood motion”, Ultrasound Med Biol 2003; 29(11):1583, both of which are hereby incorporated herein, in their entireties, by reference thereto. In these applications of BSS that are described by Gallippi et al, the principal component basis functions are calculated only for the purposes of filtering the input data matrix. Parameters are never extracted from the principal components themselves. Further, these techniques require manual inspection of the time and depth projections of the basis functions onto the input signals. Moreover, the methods described by Gallippi et al using complex data in the aforementioned reference, Gallippi et al 2002 do not estimate parameters directly from the principal components. Rather, the phases of the principal components are only used for visual inspection in order to manually determine which principal components to retain. The method used for filtering by Gallippi do not window the echo data such that the input signal is approximately stationary through range. Stationarity is used here as a statistical term meaning that the first and second order statistics of a signal are approximately constant through range. Thus, by not limiting the extent through range over which BSS operated on the input signal, the estimation of the covariance matrix and computed principal components were inaccurate in the Gallipi et al. methods.
Kruse et al. “A new high resolution color flow system using an eigendecomposition-based adaptive filter for clutter rejection”, IEEE Trans Ultrason Ferroelect Freq Contr 2002; 49(10):1384-1399(which is hereby incorporated herein, in its entirety, by reference thereto) discloses a method in which phase information is not used and signal components are not differentiated based on motion indicated by the phase of one or more principal components. Velocity cannot be estimated directly from the eigenvectors calculated in the method of Kruse et al. Rather, the technique selects a variable number of eigenvectors to retain, based on a priori knowledge of the imaging environment. This technique necessitates the calculation of all principal components, which limits computational efficiency.
Ledoux et al., “A. Reduction of the clutter component in Doppler ultrasound signals based on singular value decomposition: a simulation study”, Ultrason Imaging 1997; 19(1):1-18, (which is hereby incorporated herein, in its entirety, by reference thereto) discloses a method where phase information is not used and signal components are not differentiated based on motion indicated by the phase of one or more principal components. Furthermore, performance was not improved over other methods at low blood velocities unless ensemble lengths were increased to approximately 100 RF signals which, in practice, is not realistic. The number of basis functions corresponding to the signal of interest is not automatically obtained.
Yu et al., in “Single-ensemble-based eigen-processing methods for color flow imaging—part II. The matrix pencil estimator” IEEE Trans Ultrason Ferroelect Freq Contr 2008; 55(3):573-587 (which is hereby incorporated herein, in its entirety, by reference thereto), applies eigen-based decomposition techniques to estimate flow using a technique called the Pencil Matrix. This technique is limited to applications of color flow imaging and solves a generalized eigenvalue problem rather than finding principal components. Additional steps required for this method include the formation of a hankel matrix and matrix pencils, which reduce computational efficiency. In this method, phase information is not used and signal components are not differentiated based on motion indicated by the phase of one or more principal components.
Mauldin et al., in “Robust principal component analysis and clustering methods for automated classification of tissue response to arfi excitation” Ultrasound Med Biol 2008; 34(2):309-325 (which is hereby incorporated herein, in its entirety, by reference thereto), employs BSS with data mining techniques to automate the identification of tissue structures exhibiting similar displacement responses to acoustic radiation force excitation. This method does not improve displacement calculations but instead, operates on displacements that have already been computed using standard methods. Displacement estimation errors are therefore not reduced by use of this method.
Motion estimators are commonly classified based upon the domain in which they operate. The most common phase domain techniques are Kasai's 1D autocorrelator, see Kasai et al., “Real-time two-dimensional blood flow imaging using autocorrelation technique”, IEEE Trans Sonics Ultrason. 32:458-463, 1985, which is hereby incorporated herein, in its entirety, by reference thereto, and Loupas' 2D autocorrelator, see Loupas et al., “Experimental evaluation of velocity and power estimation for ultrasound blood flow imaging, by means of a two-dimensional autocorrelation approach”, IEEE Trans Ultrason Ferroelect Freq Contr. 42:689-699, 1995, which is hereby incorporated herein, in its entirety, by reference thereto. Both techniques were developed to measure a single velocity estimate from an entire ensemble of echo data. However, they may also be used to estimate individual displacements to form displacement profiles. The Loupas algorithm improved upon Kasai's by taking into account the local variations in the center frequency of the echo signal.
While generally requiring a greater computational load, several time-domain displacement estimators have been developed with superior performance to the technique of Loupas under certain conditions. A common time domain technique developed by Viola and Walker, e.g., see Viola et al, “A spline-based algorithm for continuous time-delay estimation using sampled data”, IEEE Trans Ultrason Ferroelect Freq Contr. 52(1):80-93, 2005, which is hereby incorporated herein, in its entirety, by reference thereto. This technique is termed spline time-delay estimation (sTDE), and operates by forming a spline representation of the echo signal. The delay between a splined, reference signal and a discrete, shifted signal can then be located by minimizing the mean squared error function.
There is a continuing need for methods and systems for estimating motion, from echo signals relevant to reference signals, that decrease the amount of echo decorrelation, relevant to existing techniques and systems, and that do not require an overly burdensome computational load. The present invention meets these needs.